For questions on dice, a small throwable object with multiple resting positions, used for generating random numbers. This makes dice suitable as gambling devices for games like craps, or for use in non-gambling tabletop games.

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Regarding combinatorics on dice…

The problem: If you are to roll a die five times, what is the probability the fifth die is not a repetition? Apparently the answer is $$\frac{6\cdot5^4}{6^5}$$ but I don't really see why. What ...
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36 views

Probability of rolling n dice to match another set of dice, d, given r rolls (like yahtzee)

(Note: I will eventually code this, but i'm primarily interested in the math behind it) I'm trying to create a function in Java to calculate the probability of getting a desired outcome from n rolled ...
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0answers
11 views

Multiple Dice Roll Probability (With Forumla)

I'm having the trouble of determining probability over multiple die rolls. I'm working with this formula. $$\frac{d20+d(\textrm{skill}) - \textrm{difficulty}}{d20+d(\textrm{skill})}$$ Basically, you ...
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2answers
26 views

Conditional probability rolling two dice

Two fair dice are rolled. What is the conditional probability that at least one lands on 6 given that the dice land on different numbers? I already know the answer, but am having some trouble ...
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0answers
25 views

Probability of rolling one die by two persons 3 times each [on hold]

So suppose you have one die. Person A rolls one die 3 times. Person B does the same after A is finished. What is the probability that person A's smallest number (of his/hers 3 rolls) is greater than ...
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1answer
23 views

How to win at a dice game using Central Limit Theory and Binomial Probability? [on hold]

I'm not too savvy in the way of statistics, so please keep this in mind with the answer. There is a dice game where a person will bet money on rolling equal to or above this number. The die rolls to ...
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1answer
32 views

Probability that less dice thrown will beat more dice thrown?

I'm trying to figure out a general equation to determine the probability that the sum of $m$ dice will be greater than the sum of $n$ dice, where $m < n$. For example, if I roll $4$ dice, what's ...
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2answers
40 views

Probability I am first person to roll a six [closed]

If I take turns rolling a die with a friend and I roll first, what is the probability I roll a 6 first?
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1answer
40 views

Expected Value question regarding rolling a die multiple times

Let's say we play a game where we can roll a die up to two times. After each roll you may take the value you rolled, or roll again. What is the expected value assuming perfect play? Intuitively (not ...
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1answer
23 views

probability between two 6-sided dice and a 12-sided die

So if we have a game with player A who roll 2 dice with 6-sides and player B with one 12-sided die what is the probability to win for the player A and the probability to have a draw game. I have make ...
2
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2answers
41 views

Why is the probability of a dice being larger then the 2nd roll the same 2nd,3rd?

I understand that the probability of the first die roll being larger then the second is 5/12. I'm having a harder time understanding why, according to a small problem I wrote, the probability of the ...
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1answer
27 views

Finding solutions to an inequality(releating to statistics)

I am trying to solve the following problem. A person rolls 3 die, what is the probability that the sum of these die is less than or equal to 9? I have built the following inequality model ...
2
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1answer
45 views

Probability when two dice rolled. Why am I getting two different answers?

This is a homework problem that I've done two different ways. The question is P(Both dice show 4 or less $\bigcap$ No dice show a 1). I first separated them out to do P(Both dice show 4 or less) ...
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1answer
32 views

Probability of at least 3 sixes with 18 dice

I am trying to logically think about this, not to just apply formulas that are readily available for similar problems. Can anyone help explain the math behind finding the probability of getting at ...
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3answers
77 views

If a fair dice is rolled $5$ times, what is the probability that some number appears more than once?

A fair dice is rolled $5$ times. Find the probability that at least one of the possible outcomes $(1,2,3,4,5,6)$ appears more than once. A hint is the Birthday Problem. I keep getting $0.9074$, but ...
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2answers
31 views

Probability of 5 dices being 6s, given that I know 3 are 6s

Imagine a game with two players who each throw 5 dice and only they can see their own dice. If we roll and I see that I have 3 sixes, what are the probabilities that there are at least 5 sixes in ...
3
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2answers
24 views

Variance and expected values by dices, how does addition work?

I have read through some stuff and I am confused now. If we have a fair die and we just roll once, the expected value is going to be 3,5 and the variance is 2,916. Well, it is easy to count by one ...
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2answers
25 views

How to calculate the probability of a die with a wild side?

So I have a 6-sided die with 5 different values in 5 of their sides. Its sixth side can be treated as any of the other 5 values. So my question revolves around which is the probability of getting any ...
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2answers
64 views

Expected value problem on dice reroll

The question is here: Roll N* 3-sided dice(0,0,1), roll them twice and choose a better result, what is the expected value? If possible I would also like an answer for dice {0,1,2} or {1,2,3} if ...
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3answers
2k views

On average, how many times must I roll a dice until I get a 6?

On average, how many times must I roll a dice until I get a 6? I got this question from a book called Fifty Challenging Problems in Probability. The answer is 6, and I understand the solution the ...
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3answers
42 views

Chance of winning simple dice game

Tossing two fair dice, if the sum is 7 or 11, then I win; if the sum is 2, 3 or 12, then I lose; if the sum is one of rest of numbers then I toss the two dices again. What is probability of winning? ...
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1answer
69 views

Expected outcome for repeated dice rolls with dice fixing

Here is another dice roll question. The rules You start with n dice, and roll all of them. You select one or more dice and fix them, i.e. their value will not ...
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3answers
37 views

Determining number of combinations on odd dice

Suppose we had four dice with four sides. Two sides have a $\frac{1}{10}$ chance of being rolled, two sides have a $\frac{4}{10}$ chance of being rolled. The dice score points equal to 1, 3, 4, and 6, ...
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1answer
40 views

Formula for X “successes” with X 10 sided die.

I am trying to create a formula for the % chance of having Y number of dice hit a number 8, 9 or 10 out of X possible. For example the chance of having 7 dice out of 10 dice be one of the 3 numbers. ...
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2answers
56 views

combinatorics dice question

There are $10$ identical dice ($1$ - $6$). How many different results can we get so that the set of results will be exactly $3$. for example: $7$ dice will be the number $2$, $2$ dice will be $3$ and ...
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2answers
31 views

An $m$ sided dice is rolled $n$ times what is the chance of getting an average of $\frac{m+1}{2}$?

If I roll a six sided dice twice there is a $1$ in $6$ chance that the results will sum up to $7$ (giving an average of $3.5$ per dice). And if I only roll it once it is not possible to get a $3.5$. ...
2
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1answer
43 views

Tetra Master Dice Rolls

In the game Tetra Master, two players play a card with a number n between 0 and 15, inclusive. Then, both players roll a 16-sided die numbered from 0 to 15. Both players than add up their dice rolls ...
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2answers
69 views

Probabilities of Dice Pools

Given 5 fair, 6-sided dice, calculate the probability of an equal or greater number of dice showing 1 appearing than the number of dice showing 4,5, and 6 combined. For example: if 5 dice are rolled ...
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2answers
42 views

Question about combinatoris of four dice

We have $4$ dice with $4$ different dyes : Green, Yellow, Red and Blue. I need to know how many options do i get so that I'll get the number $3$ at least once. These are 6 sided dice, color does ...
2
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1answer
63 views

Derivation of dice-sides polynomial

This question on PPCG.SE fascinated me. In particular @xnor's brilliant answer providing an elegant polynomial to provide the solution. In summary, the question asks for a program that, for an ...
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1answer
45 views

Four dice showing 3 values

I have 4 different color dice: blue, red, yellow and green. I need to check how many possibilities we get if the set of the numbers that are on the dices consists of 3 distinct numbers. In other ...
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2answers
178 views

A fair die is rolled $N > 6$ times. What is the probability the last 6 rolls were exactly $1,2,3,4,5,6$?

You rolls a fair die $N > 6$ times and you want to rolls the sequence $1,2,3,4,5,6$ in this order. What is the probability that the last 6 rolls were (in consecutive order) $1,2,3,4,5,6$, (So, on ...
2
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1answer
68 views

Probability Sum of One, Two, or Three out of Three Dice

I was given a problem in my stats homework that I had some trouble with. The question is as follows: If three six-sided dice are thrown, what is the probability of obtaining a four when obtaining a ...
2
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1answer
68 views

Expected number of moves of a random walk inside a simplex

Few days ago, Roger Blazey, retired head maths teacher, at LinkedIn group told about the following problem: “This problem was raised as part of a lecture at The Biennial AAMT (Australian ...
2
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2answers
242 views

Why does it seem to decrease probability to roll more times?

I am looking how to find the probability of rolling 10 sixes in 60 rolls. After reading Calculate probabilities. 40 sixes out of a 100 fair die rolls & 20 sixes out of a 100 fair die roll, it ...
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2answers
80 views

Probability of rolling a sum of N with up to infinite rolls of a die

I'm trying to figure out if there is some (relatively simple) formula for calculating the probability of rolling a sum of N with as many rolls as needed with a single regular six-sided die. For ...
2
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1answer
54 views

Dice 10000 probability of not scoring

There is a dice game I played recently, called "Dice 10,000", that is very similar to Farkle but a little simpler. In the version I played (house rules) a person scores on any given turn if they get ...
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3answers
87 views

Probability of rolling $111, 222, 333, 444, 555, 666$ in that order

What are the odds of rolling triples with $3d6$ like this: $111, 222, 333, 444, 555$, and $666$ perfectly in a row? I know that the odds of rolling triples in a row without any specific order is $36^3 ...
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3answers
583 views

Probability of some die face being missed N or more times in a row in M rolls? [Clarified]

2015/01/28 Clarification: Question rewritten to remove ambiguity that elicited (interesting) responses to a different problem (use edit should you wish to view). From Markus' feedback on the earlier ...
2
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0answers
77 views

Simulating dice by coins

Suppose you have a fair n-sided die $D_n$ - or rather suppose you don't have a $D_n$ but want to simulate one by repeatedly (but finitely many times) throwing a single (possibly biased) coin $C_p$ ...
3
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1answer
68 views

Probability that rolling X dice with Y sides and summing the highest Z values is above some value k

Some background: There is an RPG called Legend of the Five Rings, with an interesting dice system. You roll X dice, and keep the highest Z of them. You add those Z dice together. This is phrased as ...
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2answers
36 views

Permutation/Combination question on dice

Question: Three dice (six faces: each face -> number 1 to 6) are rolled. What is the number of possible outcomes such that at least one die shows number 2? My attempt: One die has to show two. ...
2
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5answers
101 views

Jamie rolls a die multiple times. find the probability that she rolls her first 5 before she rolls her second even number

Jamie rolls her fair 6-sided die multiple times. Find the probability that she rolls her first 5 before she rolls her second (not necessarily distinct) even number? This is what I have so far... ...
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2answers
57 views

Expected value of a die when decision to role again depends on previous outcome

(Introduction to Probability, Blitzstein and Nwang) A fair die is rolled some number of times. You can choose whether to stop after 1, 2, or 3 rolls, and your decision can be based on the ...
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1answer
50 views

Getting a simultaneous first $6$ with two dice

What's the probability that two players that each throw a normal dice get their first six at the same time ? Let $X_k,Y_k$ denote the numbers obtained with the first ($X$) and second ($Y$) dice at ...
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1answer
78 views

Uniform distribution of the sum of two dice

Is it possible to build two dice such that the sum of the two dice follows an uniform distribution on $\{2,\dots,12\}$ ? EDIT : Both dice must have sides 1-6, but the probability that the dice falls ...
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0answers
68 views
3
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1answer
60 views

What's the probability of rolling 10 dice each with 10 sides and each will have to same number?

I think the probability is $1\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}={1\over 10^9}={1\over ...
2
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1answer
48 views

What is the probability of not rolling any given number on 10 rolls of a die?

In other words, ALL combinations which don't contain at least one of the number from 1-6 would count. So for example... 5, 2, 3, 3, 4, 1, 5, 5, 3, 1 would be counted because there is no 6 Also 5, ...
3
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3answers
87 views

Calculating the probability that throwing two dice will yield a higher number than throwing one die

How do I work out the probability that Andy, rolling two dice, will roll a number higher than Candy, rolling one die? The highest number you can roll with one die is six. The probability of rolling ...